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Title: Oscillatory cellular patterns in three-dimensional directional solidification

We present a phase-field study of oscillatory breathing modes observed during the solidification of three-dimensional cellular arrays in micro-gravity. Directional solidification experiments conducted onboard the International Space Station have allowed for the first time to observe spatially extended homogeneous arrays of cells and dendrites while minimizing the amount of gravity-induced convection in the liquid. In situ observations of transparent alloys have revealed the existence, over a narrow range of control parameters, of oscillations in cellular arrays with a period ranging from about 25 to 125 minutes. Cellular patterns are spatially disordered, and the oscillations of individual cells are spatiotemporally uncorrelated at long distance. However, in regions displaying short-range spatial ordering, groups of cells can synchronize into oscillatory breathing modes. Quantitative phase-field simulations show that the oscillatory behavior of cells in this regime is linked to a stability limit of the spacing in hexagonal cellular array structures. For relatively high cellular front undercooling (\ie low growth velocity or high thermal gradient), a gap appears in the otherwise continuous range of stable array spacings. Close to this gap, a sustained oscillatory regime appears with a period that compares quantitatively well with experiment. For control parameters where this gap exist, oscillations typically occurmore » for spacings at the edge of the gap. However, after a change of growth conditions, oscillations can also occur for nearby values of control parameters where this gap just closes and a continuous range of spacings exists. In addition, sustained oscillations at to the opening of this stable gap exhibit a slow periodic modulation of the phase-shift among cells with a slower period of several hours. While long-range coherence of breathing modes can be achieved in simulations for a perfect spatial arrangement of cells as initial condition, global disorder is observed in both three-dimensional experiments and simulations from realistic noisy initial conditions. The, erratic tip splitting events promoted by large amplitude oscillations contribute to maintaining the long-range array disorder, unlike in thin sample experiments where long-range coherence of oscillations is experimentally observable.« less
 [1] ;  [2] ;  [1] ;  [2] ;  [2] ;  [2] ;  [3] ;  [2] ;  [1]
  1. Northeastern Univ., Boston, MA (United States)
  2. Aix-Marseille Univ. and CNRS UMR, Marseille Cedex (France)
  3. Iowa State Univ., Ames, IA (United States)
Publication Date:
OSTI Identifier:
Report Number(s):
Journal ID: ISSN 1539-3755
Grant/Contract Number:
Accepted Manuscript
Journal Name:
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Additional Journal Information:
Journal Volume: 92; Journal Issue: 4; Journal ID: ISSN 1539-3755
American Physical Society (APS)
Research Org:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Org:
Country of Publication:
United States